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A Remarkable Collection of Babylonian Mathematical Texts By Jöran Friberg

The book analyzes the mathematical tablets which are in the possession of a private collector, Martin Schoyen. This collection contains all sorts of tablets, some similar to classical ones but also others with fascinating new material. Here the author translates their mathematical content, compares it with previous known material, then evaluates the period of the tablet and its purpose. This allows the author to provide new insights into the interpretation of some classical tablets, as for example Plimpton 322 which has an exclusive appendix. What makes this book so unique is the light being shed on Babylonian mathematics. For instance, new evidence of Babylonian familiarity with sophisticated mathematical objects is provided, including the knowledge of the three dimensional Pythagorean equation and the familiarity with the geometry of the icosahedron is new and unexpected. The author is a master of analysis of the errors found in the tablets. It is well known that computational errors in the tablets are revealing of the algorithms employed in the computations. The author exploits with mastery this clever technique to gain new insight in the mathematical reasoning behind the content of the tablets. From the analysis it becomes increasingly clear that Babylonians were outstanding calculators, probably only comparable in modern times with exhibition genius calculators. For example, it appears that schoolboys were familiar with the multiplication tables at least up to 25!. He also gives numerous geometrical possible explanations and interpretations of the tablets. Another very important finding is the use of the zero notation in novel contexts and periods. The book is very carefully written and organized, the tablets are classified according to their mathematical content and purpose, while useful drawings and pictures are provided for the most interesting tablets. The author makes a great effort to make the material accessible to both assyriologists and mathematicians. There is an introduction with basic background on babylonian mathematics and on numerous occasions the author reviews basic mathematical material

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